Approach for Overcoming Numerical Inaccuracy Caused by Load Discontinuity

It was found that the discontinuity at the end of an impulse will lead to numerical inaccuracy as this discontinuity will result in an extra impulse and thus an extra displacement in the time history analysis. In addition, this extra impulse is proportional to the discontinuity value at the end of the impulse and the size of integration time step. To overcome this difficulty, an effective approach is proposed to reduce the extra impulse and hence the extra displacement. In fact, the novel approach proposed in this paper is to perform a single small time step immediately upon the termination of applied impulse, whereas other time steps can be conducted by using the step size determined from accuracy consideration in period. The feasibility of this approach is analytically explored. Further, analytical results are confirmed by numerical examples. Numerical studies also show that this approach can be applied to other step-by-step integration methods. It seems that to slightly complicate the programming of dynamic analysis codes is the only disadvantage of this approach.